# Heptagonal-cuboctahedral duoprism

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Heptagonal-cuboctahedral duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Heco |

Coxeter diagram | x7o o4x3o () |

Elements | |

Tera | 7 cuboctahedral prisms, 8 triangular-heptagonal duoprisms, 6 square-heptagonal duoprisms |

Cells | 56 triangular prisms, 42 cubes, 7 cuboctahedra, 24 heptagonal prisms |

Faces | 56 triangles, 42+168 squares, 12 heptagons |

Edges | 84+168 |

Vertices | 84 |

Vertex figure | Rectangular scalene, edge lengths 1, √2, 1, √2 (base rectangle), 2cos(π/7) (top), √2 (side edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Cope–co–cope: |

Theddip–hep–squahedip: | |

Theddip–trip–cope: 90° | |

Squahedip–cube–cope: 90° | |

Central density | 1 |

Number of external pieces | 21 |

Level of complexity | 20 |

Related polytopes | |

Army | Heco |

Regiment | Heco |

Dual | Heptagonal-rhombic dodecahedral duotegum |

Conjugates | Heptagrammic-cuboctahedral duoprism, Great heptagrammic-cuboctahedral duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×I_{2}(7), order 672 |

Convex | Yes |

Nature | Tame |

The **heptagonal-cuboctahedral duoprism** or **heco** is a convex uniform duoprism that consists of 7 cuboctahedral prisms, 6 square-heptagonal duoprisms, and 8 triangular-heptagonal duoprisms. Each vertex joins 2 cuboctahedral prisms, 2 triangular-heptagonal duoprisms, and 2 square-heptagonal duoprisms.

## Vertex coordinates[edit | edit source]

The vertices of a heptagonal-cuboctahedral duoprism of edge length 2sin(π/7) are given by all permutations of the last three coordinates of:

where j = 2, 4, 6.

## Representations[edit | edit source]

A heptagonal-cuboctahedral duoprism has the following Coxeter diagrams:

- x7o o4x3o (full symmetry)
- x7o x3o3x ()

## External links[edit | edit source]

Klitzing, Richard. "n-co-dip".